[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Swarm robotics is an approach to collective robotics that takes inspiration from the self-organized behaviors of social animals. Through simple rules and local interactions, swarm robotics aims at designing robust, scalable, and flexible collective behaviors for the coordination of large numbers of robots. In this paper, we analyze the literature from the point of view of swarm engineering: we focus mainly on ideas and concepts that contribute to the advancement of swarm robotics as an engineering field and that could be relevant to tackle real-world applications. Swarm engineering is an emerging discipline that aims at defining systematic and well founded procedures for modeling, designing, realizing, verifying, validating, operating, and maintaining a swarm robotics system. We propose two taxonomies: in the first taxonomy, we classify works that deal with design and analysis methods; in the second taxonomy, we classify works according to the collective behavior studied. We conclude with a discussion of the current limits of swarm robotics as an engineering discipline and with suggestions for future research directions.

/pdf/swarm-robotics-a-review-from-the-swarm-engineering-46mfc058e6.pdf

Swarm robotics: a review from the swarm engineering perspective

Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.

/pdf/graph-coloring-problems-4v7vijos3s.pdf

Graph Coloring Problems

: Significant progress has been made with solution of location problems and in preprocessing and decomposition for discrete optimization. There has also been research on the application of techniques from combinational optimization to nonlinear problems.

http://www.dtic.mil/dtic/tr/fulltext/u2/a273552.pdf

Discrete Applied Mathematics

Supereulerian bipartite digraphs

Energy Management System with Automatic Reconfiguration for Electric Shipboard Power Systems

In [Discrete Math. 101 (1992) 33 37], Fleischner proved that if G is a 2-edge-connected graph, then G has an even mbgraph H with a(H) > 2 such that H contains all vertices of G with degree at least 3. In {J. Combinatorial Theory, Ser. B 35 (1983) 297 308L Bermond Jackson and Jaeger showed that every 2-edge-connected graph G has an even subgraph H with JE(H)I > 3⁄4IE(G)IIn this note, we shall show that if G is a 2-edge-connected. graph, then each of the following holds: (i) G has an even subgraph H such that H contains all vertices of degree at least 3 in G and such that H contains a given pair of adjacent edges in G. (ii) G has an even subgraph H such that H contains all �ertices of degree at least 3 in G and such that IE(H)I > 3IE(G)Iraphs in this note are finite and undirected, and may have mul­ edges and loops. For a graph G, we denote O ( G) the set of :es of odd degree in G. A graph G is even if O(G) = 0. Let ,u be an edge in G. The contaction G / e is the graph obtained G by identifying the two ends of e and by deleting the resulting • For each integer i > 1, denote Di(G):::: {v E V(G): dc(u) = i} and D7(G) = Uj�iDj(G). Ising th S r :> e P itting Lemma (Lemma III.26 of [5], see also [6]) ao

/pdf/even-subgraphs-of-a-graph-1dxh18xddi.pdf

Even subgraphs of a graph

There have been researches on sufficient spectral conditions for Hamiltonian properties and path-coverable properties of graphs Utilizing the Bondy–Chvatal closure, we provide a unified approach to study sufficient graph eigenvalue conditions for these properties and sharpen several former spectral Hamiltonian results on balanced bipartite graphs and complementary graphs

Hong-Jian Lai

Papers

Supereulerian bipartite digraphs

Energy Management System with Automatic Reconfiguration for Electric Shipboard Power Systems

Even subgraphs of a graph

Unified Spectral Hamiltonian Results of Balanced Bipartite Graphs and Complementary Graphs

Graph r-hued colorings - A survey